{"paper":{"title":"Where Hindsight Credit Can Reside: A Signed-Capacity View of Token Updates in RLVR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The credit a token can carry in RLVR is upper-bounded by its entropy.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Hange Zhou, Haodong Wu, Hongyu Ge, Keyi Wu, Qihong Lin, Siyi Liu, Yongqi Zhang, Yuhang He, Zhuo Zheng, Zixin Zhong","submitted_at":"2026-04-13T06:32:49Z","abstract_excerpt":"Reinforcement Learning with Verifiable Rewards (RLVR) improves the reasoning ability of Large Language Models (LLMs), but sparse outcome rewards make token-level credit assignment difficult.\n  We study token-level credit as a reward-conditioned shift from the behavior policy to a hindsight posterior.\n  In autoregressive RLVR, this shift can be expressed through Conditional Mutual Information (CMI), which shows that token entropy upper-bounds possible hindsight credit.\n  Entropy, however, indicates capacity rather than update direction, so we introduce the Four Quadrant Decomposition to separat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We adapt Conditional Mutual Information to the autoregressive RLVR setting and prove that the credit a token can carry is upper-bounded by its entropy.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The adaptation of conditional mutual information to the autoregressive RLVR setting correctly captures the credit a token can carry, and that high-entropy tokens are the primary locus of reasoning improvements.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Token credit in RLVR is upper-bounded by entropy, with reasoning gains concentrated in high-entropy tokens, motivating Entropy-Aware Policy Optimization that outperforms baselines.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The credit a token can carry in RLVR is upper-bounded by its entropy.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"760faad15b650b36e68df48d88518293dae3236d59b670f2a19f13858e515ac0"},"source":{"id":"2604.11056","kind":"arxiv","version":2},"verdict":{"id":"232c2a53-2d87-48e3-9350-a884ce6b167d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:29:49.448633Z","strongest_claim":"We adapt Conditional Mutual Information to the autoregressive RLVR setting and prove that the credit a token can carry is upper-bounded by its entropy.","one_line_summary":"Token credit in RLVR is upper-bounded by entropy, with reasoning gains concentrated in high-entropy tokens, motivating Entropy-Aware Policy Optimization that outperforms baselines.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The adaptation of conditional mutual information to the autoregressive RLVR setting correctly captures the credit a token can carry, and that high-entropy tokens are the primary locus of reasoning improvements.","pith_extraction_headline":"The credit a token can carry in RLVR is upper-bounded by its entropy."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.11056/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ee8768e998565f82a9a18e81fffef09cde0faf3c6ef275744b7e36c13208b9c3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}